Abstract
One common procedure in solving a normalized damped linear system with non-zero off-diagonal damping elements is to replace the normalized damping matrix by a selected diagonal matrix. The extent of approximation introduced by this method of decoupling the system is evaluated, and tight upper bounds on the norm of errors are derived. Moreover, when the normalized damping matrix is diagonally dominant, it is shown that decoupling the system by neglecting the off-diagonal elements indeed minimizes the error upper bound. The results expounded in this paper are applicable to any damped linear dynamical system the coefficient matrices of which are symmetric and positive definite.
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